Hold'em Odds Calculator

Have you ever been at a table and someone talking about how they were way ahead in a hand? Want to check it out.. maybe you want them to check out to see if their math is right.... Send them here to DrCheckRaise Poker Forums.

We just added a poker odds calculator,(Courtesy of PokerNews) so that you can come here and check to see how one hands plays against another.If you scroll down the right side of the page you will find the new odds calculator. Use it.. and tell your friends and your enemies where they can find the answers to those odds questions.

I am a member of Poker News and write blogs there just like here; it is a good site. Their calculator appears to be limited to individual hands versus ranges.

I have been using Poker Stove for years. It is a free software download that you can use at anytime by creating a shortcut on your screen. It works directly from your computer without you having to go to any internet site to use it and it is free.www.pokerstove.com

When you first look at PokerStove, it appears somewhat complicated, but after a few uses and exploring its features, you will find it easy to use.

PokerStove is very versatile and allows you to not only enter specific hands for each player, but ranges. Then you can see how well your hands hold up to what you think your opponent’s range might be, since you will not, in most cases, be able to put any opponent on a specific hand.

The whole idea of knowing your opponents’ ranges gives you a starting point for knowing how to play your cards, e.g., how well do your pocket Tens hold up to his range, which includes any pocket pair, any Broadway, any suited, and unsuited Aces – should you raise. You can put those variables into Poker Stove; and, you will be surprised at how well your pocket tens hold up. Against his range, you have 68.685% pot equity. Now, if you know his/her betting patterns, SPR - Stack to Pot Ratio, fold equity, etc., you might be able to win more hands, e.g., does he always checkraise with pairs higher than tens, does he always just call with small pairs and draws, etc - so if he/she is only calling, you might shove knowing that most likely you have him/her beat because he/she has a small pair or is on a draw, which he/she might fold to a large bet.

In your example, Kings (King of spades and King of hearts) are 18.551% or 19% according to Stove – using Spade/Heart combination. These numbers are somewhat unrealistic because 10 players will all almost never have a spade/heart combination as their pocket cards. If you change the pocket Aces to Ace of Clubs and Aces of diamonds, the percentage goes up to 31% if the rest have a Spade/Heart combination.

And, the value of any two pocket cards goes down as the number of opponents goes up; they are inversely related – an inverse or negative relationship – it is not a linear (straight-line) relation because of the trillions of possible combinations that can occur based on the five cards that hit the felt (i.e., the flop, turn and river) – assuming 9 players (see poker probability (Texas hold’em) – Wikipedia. There are actually more than 21 octillion combinations, but some of these are duplicates, e.g., 2-3 versus 3-2. This is a great article on Texas Hold’em poker probability. [en.wikipedia.org])

Given the 10 hands (AA through 55), 55 is rated higher than 66, 77, and 88 because it can make more straights because the cards it needs have not been used in the nine other hands, i.e., A2345, the wheel. Same is true for the 66, but, it has 2 less cards to make a straight because two 55 are already used. Same is true for the other straights. Eights are higher because there are only 6 higher pocket pairs, Nines 5 higher pocket pairs and so on, despite having less straight possibilities. All these are related to their EVs - Another way of ranking hands that David Sklansky talks about is EV – Expected Value.

The definition of EV is :

“The term "Expected Value" (also referred to as EV or Expectation) is used a lot in poker strategy discussions, and if you've wondered what it means but never dared to ask, this is the article for you! The term originates in math (specifically probability mathematics) and is used to describe the long-term average outcome of a given scenario. In order to calculate expected value, you take every possible outcome, multiply each by the probability of that outcome happening, and then adding those numbers altogether.”[www.cardschat.com]

“Expected ValueExpected value is definitely an advanced technique, but one that is critical to understand when to take a risk that even pot odds don’t necessarily support. There is reckless aggressive, and then there is smart aggressive. Expected value is one of those concepts that will take longer for most poker players to pick up, and it is a concept that is not used often, but it’s one of those little things that makes a gigantic difference in making a lot of money and making that next step in your poker game.

Expected value can be tricky because it is more theoretical than other concepts, but this is an underlying concept that every major poker player has to understand. The concept of expected value (often shortened to ‘EV’) is the expected return on a bet.[www.pokeronamac.com]

The average EV – Expected Value or expected worth of a hand played over time in terms of big bets - that is times the Big Blind Amount for those hands is as follows. For example a pair of Aces (AA), has an average EV of 2.32, which means that if you are playing in a $5/$10 game, you will have an average expected value of $23.20 playing those Aces, but keep in mind that these EVs vary by position. For example pocket Aces on the button have an EV of 2.81 versus 2.35 under-the-gun, all these EVs can be looked up on the internet.

Please don’t read anything into these Expected Value numbers without actually knowing what they really mean. E.g., don’t assume that if you always play pocket Aces on the button that you will win 2.81 times the BB each and every time; but in the long run you will. That long run can be really long. It also doesn’t mean that you should always play pocket Aces from the button regardless of what hits the felt on the flop, turn and river, e.g., 3 suited cards or 4 suited cards hit the felt, or one pair, or two pairs, or trips and your opponent shoves all-in.[www.pokeronamac.com]

Suits were eliminated as a variable for these simple "unrealistic" cases. Also, to be more realistic, the probabilities of ties would also need to be accounted for. During actual game play, guesstimates within a percent or two of actual values is probably greatly more accurate than is needed.

I had two intentions for writing my original post. The first was to answer your question as to why pockets fives have a higher win percentage over pockets sixes, sevens, and eights in your simulation of pockets Aces through pockets fives where the first card is a spade and the second a heart. Again, it is because of the number of straights that can be completed given the remaining cards. Given your scenario, more cards are available to create straights with pocket fives. Pocket sixes have a slight edge over pocket sevens for that same reason. And, yes ties do occur, but, they are insignificant and represent only 0.13%

My second intention was to acquaint our fellow members to Poker Stove, which I am sure most know about. While I appreciate the sharing of this Poker News calculator with our members, there is much better software available as a free download – Poker Stove. Poker Stove is a poker utility which facilitates equity calculation using ranges of hands, or hand distributions. After downloading Poker Stove, you can create a shortcut on your computer screen for quick access, which saves you time. It is much faster to use Poker Stove on your own computer than to go to Poker News or this site to punch in your numbers. Why go on the internet to get results when they are at your immediate fingertips using Poker Stove right on your computer?[www.pokerstove.com]

Then your follow-up comment: “In a game, guesstimates within a percent or two of actual values are probably greatly more accurate than is needed.” Axman.

Your simulation using the Poker News calculator and my simulation using Poker Stove are both simulations that used hundreds of thousands of hands in the calculations. When the results involve that many calculations, rounding results up to the nearest percent is misleading because it does not show the number of hands that were actually won, and implies that the results are almost equal, when in fact, they are not, e.g., saying that pocket fives and sixes are actually both 5% because of rounding – that is a very inaccurate statement, even in your example.

The simulation I ran on Poker Stove had 201,376 total hands played; whereas, the Poker News software does not tell you how many hands were used in their simulation. The following are the results from Poker Stove for pocket fives through eights given your scenario:

Fives - win % - 4.90% - 9,858 wins

Sixes – win % - 4.50% - 9,070 wins

Sevens - win % - 4.23% - 8,520 wins

Eights - win % - 4.60% - 9,262 wins

I also wanted to acquaint the members to the concept of EV– Expected value, which should be the starting point for all poker decisions. You want to play in situations where you have a positive EV (where you will win money), and avoid situations where you have a negative EV (will lose money) if you goal is to make the most money. The concept of EV – Expected value is important when evaluating your two pocket cards, but is only a starting point. And, there are situations where you might play pocket cards with a negative EV, e.g., A-7 unsuited, if you can see the flop cheaply and are playing a style other than TAG – Tight Aggressive Poker, e.g., if you are using a technique called “small ball poker.”

GWL666 Wrote:-------------------------------------------------------> I had two intentions for writing my original post.> The first was to answer your question as to why> pockets fives have a higher win percentage over> pockets sixes, sevens, and eights in your> simulation of pockets Aces through pockets fives> where the first card is a spade and the second a> heart. Again, it is because of the number of> straights that can be completed given the> remaining cards. Given your scenario, more cards> are available to create straights with pocket> fives. Pocket sixes have a slight edge over> pocket sevens for that same reason. And, yes ties> do occur, but, they are insignificant and> represent only 0.13%

Good point about 77 being limited by the number of straight possibilities.

[snip-snip]

> Then your follow-up comment: “In a game,> guesstimates within a percent or two of actual> values are probably greatly more accurate than is> needed.” Axman.>> Your simulation using the Poker News calculator> and my simulation using Poker Stove are both> simulations that used hundreds of thousands of> hands in the calculations. When the results> involve that many calculations, rounding results> up to the nearest percent is misleading because it> does not show the number of hands that were> actually won, and implies that the results are> almost equal, when in fact, they are not, e.g.,> saying that pocket fives and sixes are actually> both 5% because of rounding – that is a very> inaccurate statement, even in your example.>> The simulation I ran on Poker Stove had 201,376> total hands played; whereas, the Poker News> software does not tell you how many hands were> used in their simulation. The following are the> results from Poker Stove for pocket fives through> eights given your scenario:>> Fives - win % - 4.90% - 9,858 wins>> Sixes – win % - 4.50% - 9,070 wins>> Sevens - win % - 4.23% - 8,520 wins>> Eights - win % - 4.60% - 9,262 wins

[snip-snip]

Your calculations prove my suspicions. If a calculator is rounding numbers to a whole number, then 55, 66, and 88 appear to have the same probability of winning (5%), in these particular, if unrealistic, cases. Your point is well taken about the problem with rounding, but it's up to the calculatee to decide what level of precision best suits their needs. Remembering it is close to 5% may be sufficient.

By use of the term "guesstimate", I was referring to in-game calculations done in your head, or from memory. Of course, some info input to a calculator may be no better than a guesstimate.

Not mad. Just trying to help the reader see which comments were made by whom--but I can unbold them if you like.

So, ALL CAPS IS SHOUTING, and all bold is being mad? Knew about the stigma with the former. but was unaware of the second.

To be continued...

Oh, yes, you said, "And, you missed the point about your 5% when dealing with large numbers, as in probability theory."

Actually, I think you are missing my point. You are trying to deal with this from a theoretical viewpoint. Just use your common sense. I am trying to point out the practical application of probabilities in real-world situations. Most poker players don't need to know the probabilities to an gazillion number of places beyond the decimal point. Knowing that something is 5% and not 50%, is probably close enough for a lot of people, if they even think about it.

However, your calculations do point out that there are some differences in the numbers that some people may be interested in knowing. So, kudos to your analysis.

Axman, I don’t know if bolding everything has a meaning, but now it does.

As for theoretical, poker analysis software is all about theoretical probabilities, which deal in large numbers and percentages expressed at least out two or more decimal points, usually at least three, e.g., 45.837%.

Does it make any difference if I know pocket aces (Ace of spades, Ace of Hearts) are an 81.06% favorite to win against pocket kings (King of clubs, King of diamonds) that have 18.55%, or if I round to 81% versus 19% in a heads-up confrontation before the flop. Not really, I never said it did. But who cares, I hope everyone knows that pocket Aces, usually beat pocket Kings without using poker software.

But, that brings up another point about the Poker News hand-analysis software – what is it really good for? If I watch a hand and a guy says he was way ahead, but he loses; I know exactly why he lost. What I don’t know is why that player would make such an outlandish statement, unless he had the nuts, which he obviously did not because he lost.

Any poker player who actually says he was way ahead in any hand either has the nuts or a crystal ball or is just too stupid to know any better.

Any time a player calls your raise, you are either way ahead or way behind. Even if you start with pocket aces and have a dead uncoordinated board, saying you are way ahead is meaningless, unless you have a Royal Flush.

Whenever a knowledgeable poker player, a professional, says he thinks he has the best hand or is ahead, his statement is usually based on the range of hands he believes his opponent will play and what he knows about that opponent, e.g., betting patterns, player type, e.g., loose, tight. How do these professionals know how well their pocket cards will hold up against their opponent’s range of starting hands?

They use poker analysis software that allows them to enter hand ranges, e.g., Poker Stove. For example, if I have pocket tens, and am playing against a somewhat loose player that I know will play any pocket pair, any Broadway, and any suited. How to my pocket tens hold up to his range. Using, the Poker News calculator, I can’t figure that out; but using Poker Stove, I can.

Using Poker Stove, I find that my pocket tens have a 60% win percentage against his range. That information is valuable when I play against that opponent. Of course, I must know a lot more about that opponent, and see how the hand proceeds on the flop, turn, and river. But, at least I am not shooting in the dark.

I don’t know how many members read the hand analyses in Card Player magazine where players explain why they played particular hands the way they did. These professionals all talk about the hand ranges they put their opponents on, as well as other variables. How do they know that information? Well, they have watched that opponent and know his range. And, they have already used hand analysis software, e.g., Poker Stove that allows them to enter hand ranges their opponents might play against cards they might hold. They have used Poker Stove, for example, to run many simulations based on many scenarios. They have memorized the results. So when they play new opponents, and figure out their ranges, they know how those ranges will stand up against their cards. These hand analyses are important in games where money is wagered.

The analyses in Card Player magazine are in games where money is at stake. You will never see these type analyses done on hands played at subscription sites. Why? Because it is pointless, in most cases, to put your opponents on hand ranges. It is pointless because nothing is at risk, and many of your opponents will call large bets with junk hoping to hit miracles. This does not happen in the real cash world, usually; and, yes it does happen, but not with the frequency that occurs at subscription sites where many are trying to chip up early with almost anything so that have enough chips to last till they are in the money. It cost them nothing to do this, so why not do it.

Don't believe most things most poker players say at the table, especially after getting their a**es handed to them--they're usually just trying to soothe their egos (to paraphrase Bill Rini, Bill's Poker Blog).

That quote is so on the money. Some call it the crying towel. These same people think that someone actually gives a damn that they lost, and that they are always getting bad beats.

No one really gives a damn if you lost to what you think was a bad beat. Actually, the whole concept of “bad beats” has no mathematical reality, other than that bad beats have a lower mathematical probability of happening.

Are you somehow entitled to something more because your quad Aces got beat by a Straight Flush or Royal Flush? Nope! But, some online poker sites that make gazillions in profits do offer bad-beat jackpots to keep you playing so that they will continue to make egregious profits from too high rake rates and fees, with minuscule rakeback.

The phrase “bad beat” was invented, just like “bad luck” to help some people cope with their losses. Not sure why they need excuses like “bad beat” or “bad luck” to explain why they lost at anything, but some feeble, sniveling, whining types lacking personal fortitude without a modicum of common sense most blame something for their failures at poker.

Now, blaming the Poker Gods is perfectly acceptable because everyone knows they are real. The poker commandments were original written on clay tablets thousands of year ago and passed on through the prophet Doyle who faithfully transcribed the poker commandments in Doyle’s “Super System”, the Holy Bible of Poker; but you must have faith; praying is optional.

On gunsmoke yesterday a hand like GWL discribes happened. One player had 4 aces but he didn't have enough money to call so he went to the bank and borrowed money on his hand. The fool at the bank loaned him money to play the hand. Of course the other player had a straight flush. But as it turns out both was in cohoots to rob the bank without a gun. And of course Matt caught on and arrested them and got the money back for the bank.

I SOOOO wish we had a 'LIKE' button here.... Consider it ''Clicked''.....DOC